The EnKF can be interpreted as a mean-field particle approximation of a conditional McKean-Vlasov diffusion (the K-B diffusion). This latter diffusion shares the same law
as the filter associated to the linear and Gaussian model in continuous-time. Hence a possible alternative to recursively solving the K-B and Riccati equations
is to generate \(N\in \mathbb {N}\)  independent copies from the K-B diffusion and use a simple Monte Carlo estimate for expectations with respect to the filter. However, the diffusion process
cannot be simulated exactly, but can be approximated in a principled way by allowing the \(N\)  samples to interact; precise details are given in Section .
The resulting method, named the Ensemble Kalman-Bucy Filter (EnKBF), is by now rather well-understood with several contributions on its convergence (as \(N\rightarrow \infty \) ) analysis; see for instance [1]}, [2]}, [3]}, [4]}, [5]}.
